Coll. Antropol. 30 (2006) 3: 607–613
Original scientific paper
Modeling the Influence of Body Size on
Weightlifting and Powerlifting Performance
Goran Markovi}1 and Damir Sekuli}2
1
2
Faculty of Kinesiology, University of Zagreb, Zagreb, Croatia
Faculty of Natural Sciences, Mathematics and Education, University of Split, Split, Croatia
ABSTRACT
The purpose of this study was to examine 1) if lifting performance in both the weightlifting (WL) and powerlifting
(PL) scale with body mass (M) in line with theory of geometric similarity, and 2) whether there are any gender differences
in the allometric relationship between lifting performance and body size. This was performed by analyzing ten best WL
and PL total results for each weight class, except for super heavyweight, achieved during 2000–2003. Data were analysed
with the allometric and second-order polynomial model, and detailed regression diagnostics was applied in order to examine appropriateness of the models used. Results of the data analyses indicate that 1) women’s WL and men’s PL scale
for M in line with theory of geometric similarity, 2) both WL and PL mass exponents are gender-specific, probably due to
gender differences in body composition, 3) WL and PL results scale differently for M possibly due to their structural and
functional differences. However, the obtained mass exponents does not provide size-independent indices of lifting performances since the allometric model exhibit a favourable bias toward middleweight lifters in most lifting data analyzed.
Due to possible deviations from presumption of geometric similarity among lifters, future studies on scaling lifting performance should use fat-free mass and height as indices of body size.
Key words: allometric scaling, body size, muscle strength, polynomials, powerlifting, weightlifting
Introduction
Muscle strength has been defined as the maximum
force or torque developed during maximal voluntary contraction under a given set of conditions1. Although performance in almost every sport depends on certain amount of muscle strength2, this is particularly emphasized
in two sporting activities: weightlifting3 and powerlifting. In both sports, the objective is to perform maximum
lifts using different lifting techniques. Three events make
up the sport of powerlifting (PL): bench press, squat, and
dead lift. Weightlifting (WL) consists of two events: snatch,
and clean-and-jerk. By summing the results in each lifting event, a total result can be calculated, which is usually used as a criterion of overall lifting (or strength) performance in both WL and PL.
It is well known that body size represents an important factor that affects muscle strength1,4,5. In particular,
there exists significant positive relationship between muscle strength and body size1. In order to eliminate the effects of body size on lifting performance, athletes in both
sports compete in different weight classes. However, in
weightlifting competitions comparisons are often made
among lifters who win the different weight classes so
that the best lifter in the competition can be identified6.
In order to be able to compare results of lifters from different weight classes, the results should be appropriately
normalized for body mass (M).
The simplest method of normalizing muscle strength
(or any other physiological or performance variable) is to
divide the result (in this case mass lifted) with subjects’
M, i.e. ratio standard7–9. However, for this ratio standard
to be valid the true relationship between two variables
should be linear and the regression should pass through
the origin. Unfortunately, in WL and PL neither of these
two conditions is satisfied, so this scaling method is
inappropriate8–11. In particular, many studies (see Jaric1
for review) have shown that muscle strength (and lifting
performance) appears to increase at a lower rate than M.
Therefore, ratio scaling have been shown to penalize
heavier individuals because too much an adjustment
would be made for M thus disproportionately »deflating«
the overall result of heavier individuals10,11.
Received for publication June 5, 2004
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G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
The theoretical explanation for these results is based
on the presumption of geometric similarity10, by which
muscle strength should be proportional to muscle physiological cross-sectional area – which is proportional to M2/3
– rather than M7,13. Therefore, other scaling models, the
allometric model in particular, have been proposed and
used frequently6,7,14–16. Allometric modelling is based on
the assumption that the true relationship between depended variable (in this case, muscle strength) and an independent anthropometric variable (in this case, body
mass) is curvilinear and passes through the origin (for
review see Nevill and Holder9). Specifically, it presumes
an allometric relationship:
S = a · M b,
(eq. 1)
where S is muscle strength, M is body mass, b is the allometric exponent and a is constant multiplier. When allometric exponent b is determined, muscle strength (in this
case mass lifted) could be expressed independent of M:
Sn = S / Mb,
(eq. 2)
where Sn represents normalized muscle strength. Note
that Sn corresponds to constant multiplier a (for details
see Jaric1 and Jaric et al.4).
This approach has been frequently applied in normalizing WL and PL performance6,7,10,11,17–21. However, while
several studies have determined that the overall WL and
PL results should scale with a theoretical mass exponent
b = 0.676,11,20, some studies showed that the allometric
exponent b in the WL lifting is considerably lower than
0.67, predicted by the presumption of geometric similarity10,17. In contrast, some researchers that modelled
the total PL performance (e.g., Vanderburgh and Dooman21) reported mass exponent b significantly higher
than 0.67.
Batterham and George10 have also shown that body
composition represents an important factor in determining the relationship between muscle strength and body
mass. By excluding the subjects heavier than 91kg from
their analysis, the authors obtained allometric exponent
b = 0.68, instead of b = 0.48, when all weight categories
were considered in analysis. It must also be noted that
the majority of studies analyzed men’s lifting performance6,7,17,20 and used a rather small samples (306,7,10,11,17,19).
Jensen et al.22 have elegantly shown that sample size
represents an important factor in determining a true relationship between physiological variables and body size.
Recently, Kauhanen et al.8 analysed WL performance –
body mass relationship on large data sets of elite WL results (n = 1572) and demonstrated that the overall lifting performance does not scale with theoretically predicted exponent 0.67 (b = 0.55; 95% confidence interval
0.53–0.56). When heaviest weight class was excluded
from their analysis, mass exponent b was 0.60 (95% confidence interval 0.53–0.66), still significantly lower (p <
0.05) than 0.67. However, one possible confounding factor might be included in the study of Kauhanen et al.8.
Namely, the authors included in an analysis men’s lifting
results from 1973 to 1999. Due to increased use of anabolic-androgenic steroids and other anabolic stimulus am608
ong strength athletes in the mid 1970s and early 1980s23,
possible increase in upper limits of lean body mass could
significantly influence to the relationship between lifting
performance and body mass10.
This brief literature review suggests that different results obtained in previous studies could be the result of:
a) differences in body compositions among lifters (lifters
in heaviest category may be heavier because of excess
body fat); and b) small sample size studied. In addition to
these divergences, recent findings have indicated that
second-order polynomial model provides a superior fit to
elite WL and PL results than allometric model7,10,24,25.
For this reason, Batterham and George10 suggested that
the allometric modelling should be applied only when all
underlying model assumptions (i.e., regression diagnostics) have been rigorously evaluated and satisfied. Finally, there is an obvious lack of empirical data in scientific
literature about the relationship between lifting performance and body size in female athletes. To further examine if lifting performance scale with the theoretically predicted exponent b = 0.67, and whether there are any
differences in scaling lifting performance for body size
between genders, we analyzed lifting performance on a
relatively large sample of elite men and women weightlifters and powerlifters using both allometric and second-order polynomial model.
Materials and Methods
Performance and body size data
In this study the WL and PL data from 2000 to 2003
were analyzed. The data for WL were selected from results made in the World Championships and Olympic
Games during 2000–2003 with the respective body mass
measured at the official weigh-in before each competition
(official web-site of the International Weightlifting Federation; www.iwf.com). The data for PL were selected
form PL results made in the World Championships during
2000–2003 with the respective body mass (M) measured
at the official weigh-in before each competition (official
web-site of the International Powerlifting Federation;
www.powerlifting-ipf.com). Although both the WL and
PL consists of several lifting disciplines (see Introduction), we focused only on the total results (the sum of results in each lifting discipline) as a criterion of overall
lifting performance.
Subjects
For WL, best 10 two-event total results (sum of snatch
and clean-and-jerk) for each men and women weight category, except for super heavyweight (men’s +105 kg and
women’s +75 kg), achieved during 2000–2003 were used
in this study. If the same lifter had more than one result
in top 10 results, only his/her best result was used in further analysis. For PL, best 10 three-event total results
(sum of squat, bench press, and dead lift) achieved during 2000–2003 for men’s categories up to 110 kg, and
women up to 75 kg were used in this study. As for WL, if
G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
Data analyses
To examine if lifting performances scale with theoretically predicted mass exponent 0.67, an allometric or
power function model was applied (see eq. 1). A regression technique applied on the log-transformed data provided the values of the allometric exponent b for each lifting result (see Batterham and George10 for details of the
method). In short, a log-transformation of the presumed
allometric relationship (see eq. 1) between lifting performance S and body mass M gives:
a)
ln S = ln a + d(G ln M) + cG + b ln M + ln e, (eq. 4)
A significant gender-by-ln M interaction term (p <
0.05) for both WL and PL results was found. Therefore,
separate allometric exponents for men and women in
both lifting disciplines were calculated. Allometric exponents were reported as mean ± standard error (mean ±
SE), allowing construction of 95% confidence intervals
(95% CI).
In addition, a second-order polynomial model was also
applied to the same data, as recommended by Batterham
and George10:
(eq. 5)
The differences in the lifting performance-body size
relationship between allometric and second-order polynomial model were computed using two-tailed t-test for
testing differences between two dependent correlation
coefficients. A detailed regression diagnostics recommended by Nevill and Holder9 and Batterham and George10 was used to examine model fit. In brief, normality
of the distribution of the residuals in both analyses was
ascertained using the Kolmogorov-Smirnov test. The homoscedasticity of data (constant error variance) was tested by calculating a correlation between the raw residuals
and ln M. Appropriateness of log-linear regression model
was checked via detailed inspection of the scatter plot of
residuals and ln M.
Men's WL
460
410
Women's WL
R2 = 0.96 (0.98)
360
310
260
(eq. 3)
where ln a and b, respectively, correspond to the intercept and slope of the regression line fitted through the
logarithmic values of the experimentally recorded lifting
results and body mass, and e is an error term. Normality
of log-transformed variables was confirmed using a Kolmogorov-Smirnov test (p > 0.3). Commonality of slopes
of the lifting result-body mass relationships between men
and women were tested by including gender and gender-by-ln M interaction term in a multiple log-linear model,
as described by Batterham and George10:
S = a + bM +cM2,
Figure 1 depicts the scatter plots of M vs. lifting performances by gender in both WL (Figure 1a) and PL (Figure 1b). As expected, absolute indices of lifting performance and M suggest a strong positive relationship. The
plotted relationships are curvilinear, similar to those reported by Batterham and George10 and Vanderburgh and
Batterham11 for the WL and PL results, respectively.
R2 = 0.85 (0.87)
210
160
40
55
70
85
100
Body mass (kg)
b)
Men's PL
Women's PL
1130
1030
R2 = 0.92 (0.94)
930
Total (kg)
ln S = ln a + b ln M + ln e,
Results
Total (kg)
the same lifter had more than one result in top 10 results, only his/her best result was used in further analysis. The greatest weight category in WL, and categories
over 110 kg for men and over 75 kg for women in PL
were omitted in order to avoid possible confounding effect of body composition common in super heavyweight
categories10,11.
830
730
630
530
R2 = 0.90 (0.89)
430
330
40
55
70
85
100
115
Body mass (kg)
Fig. 1. Scatter plot of total lifted in weightlifting (a) and powerlifting (b) vs. body mass for men and women. Both allometic (solid
line) and second-order polynomial curve (dashed line) fits are
displayed together with their corresponding coefficients of determination R2 (R2 for second-order polynomial models in parenthesis).
The results of the allometric and the second-order
polynomial model applied to the lifting performances are
shown in Tables 1 and 2. The resulting solutions explained between R2 = 85% and R2 = 96% of the variation
in lifting performances analyzed in this study. Although
the second-order polynomial model explained 2% more
variance than allometric model for most lifting performances, this improvement was not significant (p>0.05).
The obtained slopes of the regression lines correspond
to allometric exponents b needed to assess body mass in609
G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
TABLE 1
ALLOMETRIC MODEL RELATIONSHIPS FOR WEIGHTLIFTING
(WL) AND POWERLIFTING (PL) PERFORMANCE (S) TO BODY
MASS (M)
N
b
TABLE 2
SECOND ORDER POLYNOMIAL MODEL RELATIONSHIPS
FOR WEIGHTLIFTING (WL) AND POWERLIFTING (PL)
PERFORMANCE TO BODY MASS (M)
95% CI
Equation
Equation
Men’s WL
S= –0.037M2 + 8.68M – 71.77
70
0.61±0.02
0.58 – 0.64
S=25.56M0.61
Women’s WL 70
0.68±0.04
0.62 – 0.76
S=13.85M0.68
Women’s WL
S= –0.068M2 + 10.76M – 169.11
Men’s PL
0.69±0.02
0.65 – 0.74
S=36.31M0.69
Men’s PL
S= –0.081M2 + 20.04M – 232.37
0.74 – 0.87
S=19.11M0.80
Women’s PL
S= –0.070M2 + 15.59M – 151.16
Men’s WL
90
Women’s PL 80
0.80±0.03
N – number of subjects, 95% CI – 95% confidence interval, b –
allometric parameter (X±standard error)
S – normalized performance
dependent indices of lifting performance (see parameter
b in eq. 3). These allometric exponents b (Table 1) represent the main result of the study. The exponents of 0.68
and 0.69 for women’s WL and men’s PL data are similar
to the theoretical prediction of 0.67. In contrast, 95%
confidence intervals of the mass exponents b for men’s
WL and women’s PL performance do no not include the
value of 0.67, suggesting that these lifting performance
scale with negative and positive allometry, respectively. It
must also been pointed out that women’s mass exponents b were significantly higher (p<0.05) than men’s
exponents in both lifting sports (see Methods section for
details).
All residual errors from fitting both models were
found to be acceptably normal when using Kolmogorov
Smirnov test (p>0.4). In addition, no linear relationship
was found between residual scores and body mass for
allometric modelling (correlation coefficients r ranged
between –0.11 and 0.09, p>0.05), suggesting that the
model errors displayed homoscedasticity.
The presented data suggest that both models demonstrated excellent fit to the lifting performances analyzed.
a)
b)
0.1
0.1
0.05
Raw residual
Raw residuals
0.05
0
R2 = 0.59
p < 0.05
–0.05
–0.1
3.9
c)
4.1
4.3
ln body mass
4.5
0
–0.05
–0.1
3.8
4.7
d)
4
4.1
4.2
4.3
4.4
0.15
0.1
Raw residuals
0.1
Raw residuals
9.3
ln body mass
0.15
0.05
0
–0.05
R2 = 0.23
–0.1
–0.15
3.8
R2 = 0.20
p < 0.05
4
4.2
4.4
ln body mass
4.6
0.05
0
–0.05
R2 = 0.02
p > 0.05
–0.1
4.8
–0.15
3.7
3.9
4.1
ln body mass
4.3
Fig. 2. Scatter plot of raw residuals vs. ln body mass for allometric model applied to: (a) men’s weightlifting results, (b) women’s
weightlifting results, (c) men’s powerlifting results, and (d) women’s powerlifting results. Second-order polynomial curve fits are displayed (solid line) together with associated coefficient of determination (R2).
610
G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
However, a detailed inspection of scatter plots of residuals vs. ln M (Figure 2) shows a curvilinear relationship
for all allometric models, except for women’s PL results.
In particular, a moderate to strong non-linear relationship was found between raw residuals and ln M (R2
=0.20–0.59, p<0.05) for men’s and women’ WL and
men’s PL performances. These results clearly indicate
that the allometric model applied to all lifting performance, except in women’s PL, exhibit a favourable bias
toward lifters in middleweight classes.
Discussion
The present study examined the allometric and second-order polynomial relationship between lifting performances in both WL and PL on the one hand, and M on
the other. Performance in WL and PL certainly represent
the maximum of achievable physical strength, so that it
seems justified to call these performances 'maximal
strength’25. The theory of geometric similarity suggests
that maximum muscle strength (S) should scale to M to
the 2/3 power (i.e., S M0.67), also known as isometric
scaling1,6. In our study, mass exponents b for the men’s
and women’s WL performances were 0.61 and 0.68. For
PL performances, gender-specific mass exponents b were
0.69 for men and 0.80 for women. While women’s WL
and men’s PL performance appeared to scale in line with
theory of the geometric similarity, men’s WL performance scale with negative allometry, and women’s PL
performance scale with positive allometry, respectively.
Modelling both WL and PL results in this study did
not include men over 105 kg (over 110 kg for PL) and
women over 75 kg. Therefore, possible confounding factor of disproportionate increase in body fat, common in
the overweight subjects 26,27 (i.e., super heavyweight categories), was excluded from the analyses. In addition, a
relatively similar number of lifting performances (between 70 and 90) was analyzed in both WL and PL. Still,
the obtained mass exponents varied from 0.61 to 0.80,
suggesting that other factors than body composition and
sample size might have had significant influence on the
lifting performance – body mass relationship. Comparisons of the allometric exponents b obtained in this study
also raised two important questions: a) Why do women
have significantly higher mass exponents in both WL and
PL than men, and b) Why do PL performances have significantly higher mass exponents than WL performances?
Regarding the first question, significantly higher mass
exponents obtained in the women’s WL and PL results
can be attributed to several factors. First, it must be underlined that WL and PL for women is a relatively new
sport event, when compared to men’s WL and PL. For example, 72 men’s and only 15 women’s World Championships in WL were held until the present date. It is, therefore, feasible to expect that men’s lifting performance
exhibit more homogeneity within body weight classes.
Figure 1a confirms this assumption, showing greater dispersion in WL results of women than of men. Thus, defined heterogeneity in strength across body weight clas-
ses in women can decrease the possibility to define a true
relationship between lifting performance and M. The
second explanation is based on the fact that women generally tend to have less active muscle mass28 and more fat
tissue (i.e., different body composition) than men29–31 regardless of the body-weight class analyzed. Moreover, it
has been demonstrated that women generally have more
fat-free mass in their lower body than men do. It is therefore, likely that the observed gender-specific relationship
between muscle strength and M could be the result of
gender differences in body composition and regional distribution of contractile tissue. Finally, one cannot exclude possible use of illegal but non-detectable drugs of a
higher prevalence among one gender over another (e.g.,
growth hormones11).
Regarding the second question, the authors recognize
two possible explanations for PL performances having
significantly higher mass exponents than WL performances. The first explanation is related to technical and
biomechanical differences between WL and PL events.
Namely, WL events (snatch and clean-and-jerk) are far
more complex movement patterns than PL events (bench
press, squat and dead lift). Therefore, besides raw muscle
strength, specific lifting skill has a profound influence on
the performance in WL. It is not uncommon that a
weightlifter misses the maximum lift due to a small technical error at the end of the lift (e.g., loss of balance). In
that case, athlete’s overall lifting performance would not
represent his/her true maximum strength capabilities.
Since characteristic motor-skill influences WL performance more than PL performance, the stated differences
in the relations between M and performances are easy to
follow.
It must also be pointed out that the WL performance
depends on several other motor abilities besides strength,
like power, speed, flexibility and coordination, which do
not scale with M similarly as muscle strength. Several
authors7,10,32 have pointed out that the WL performances
should be recognised as a combined measure of strength,
power and skill, while PL performance is a pure measure
of strength. Thus, lower mass exponent b for the WL performance when compared to the PL performance could
be the result of the abovementioned structural and functional differences between these two lifting techniques.
The second explanation is related to grip strength.
Namely, in both WL disciplines (snatch and clean-and-jerk) an athlete pulls the barbell up from the floor by
holding it with his/her palms. It can be, therefore, expected that grip strength may be one of the limiting factors for success in WL. In PL, only one lifting discipline is
related to grip strength – it is dead lift. Thus, the overall
performance in PL is probably to a smaller degree influenced by the grip strength than the performance in WL.
Vanderburgh and Batterham11 also reported similar finding. Since grip strength scales to M with negative allometry in both men and women15,16, differences in mass
exponent b between WL and PL could be also the result
of the specific influence of grip strength on lifting performance in WL and PL.
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G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
Another important finding of this study is related to
regression diagnostics of the allometric and second-order
polynomial model applied to the WL and PL data. Analysis of residuals showed that allometric modeling for M
does not provide an appropriate fit for men’s and women’s WL and men’s PL results. In particular, the results
have shown that the allometric modeling exhibit a favourable bias toward athletes in middleweight classes.
Results of the present study also confirmed previous
findings10,21 that the second-order polynomial model provides statistically superior solution when modeling lifting performances for differences in M. However, in agreement to the results of Vanderburgh and Dooman21, the
authors have found no satisfactory explanation for the
superiority of the second-order polynomial model other
than its better statistical fit. Several research studies10,11,21 have demonstrated that allometric modeling is
statistically incorrect when used to scale the WL and PL
performances for M. However, as far as we could ascertain, most researchers did not provide a possible biological explanation for the results obtained. Vanderburgh
and Batterham11 revealed that half as many powerlifters
are found in the lightest and heaviest weight classes as in
the intermediate classes and that intermediate classes’
top lifters are perhaps more likely to achieve at a higher
body mass adjusted level than those powerlifters in lower
and higher classes. However, this explanation cannot be
applied to the WL results.
A possible biological explanation for an inappropriate
fit of the allometric model in the WL and PL performances could be related to a violation of the presumption
of geometric similarity among lifters. For example, it is
common that lifters in both sport events move to a
higher weight class by increasing his/her muscle mass,
especially in the middleweight classes. In this case, lifters
with similar heights and other linear body dimensions
would have disproportionately greater limb girths and
body masses. It would be, therefore, advisable to include
more anthropometric measures (e.g., height) in the analysis when modeling lifting performance (or any other
physiological or performance variable) for differences in
body size as suggested by Nevill33. Recently, Ford et al.34
have shown that muscle mass, but not M, varies almost
exactly with the cube of height over the entire range of
body size of weightlifters, so that strength varies almost
exactly with height squared or with muscle mass to the
two-thirds power. Ford et al.34 have also showed that the
fraction of M devoted to non-contractile tissue increases
abruptly in heavier lifters. This abrupt transition produces corners in the curves relating performance variables to M, and these corners preclude a good fit by any
continuous allometric function relating a power of M to
measures of strength34. More recently, Nevill et al.35,36
612
provided evidence that athletes’ physiques could substantially deviate from geometric similarity and concluded that this deviations have serious implications for
the allometric scaling of physiological and performance
variables. In particular, Nevill et al.35,36 proposed the use
of corrected limb girths (e.g., thigh, calf) instead of M in
the allometric scaling of human biological functions.
These data suggest that other indices of body size, like
height, fat-free mass or muscle mass should be used
when modeling muscle strength for body size.
Conclusion
To summarize, our result together with some previous data8,10,11,21 indicate that the allometric modeling of
WL and PL results for M does not provide size-independent index of lifting performance. Instead, it exhibits a favourable bias toward middleweight lifters in most lifting
data analyzed. The possible explanations for this inappropriate statistical fit of the allometric model applied to
the WL and PL data are: 1) lifters have disproportionately greater limb girths than bone lengths, thus violating the presumption of geometric similarity, and 2) muscle mass does not represent a constant proportion of
body mass within the sample of elite lifters. Moreover, we
demonstrated that WL and PL results scale differently
for M possibly due to their structural and functional differences (i.e. PL is a pure strength sport, while WL is
strength-speed sport with strong emphasis on specific
and rather complex lifting skill). Finally, we showed that
the allometric relationship between lifting performance
in both WL and PL is gender-specific, probably due to
gender differences in body composition and regional distribution of contractile tissue. Based on these results we
suggest using muscle mass (or fat-free mass) and height
as indices of body size when modeling WL and PL performances. This would allow comparisons of size-independent lifting performance (separately for WL and PL) of all
lifters, regardless of weight category (i.e. super heavyweight athletes included) and gender. These findings together recent observations obtained on other human
populations35,38,39 highlight the importance of using more
suitable indices of body size than M when comparing
physiological performance of humans of different body
size.
Acknowledgments
The authors wish to thank the reviewers for their
constructive comments and critiques. This study was
supported in part by grant from Croatian Ministry of Science, Education and Sport.
G. Markovi} and D. Sekuli}: Modeling Lifting Performance for Body Size, Coll. Antropol. 30 (2006) 3: 607–613
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G. Markovi}
Faculty of Kinesiology, University of Zagreb, Hova}anski zavoj 15, 10000 Zagreb, Croatia
e-mail: [email protected]
MODELIRANJE UTJECAJA VELI^INE TIJELA NA NATJECATELJSKE REZULTATE U
OLIMPIJSKOM DIZANJU UTEGA I »POWERLIFTINGU«
SA@ETAK
Glavni cilj ovog istra`ivanja bio je utvrditi 1) da li natjecateljski rezultati u olimpijskom dizanju utega (WL) i »powerliftingu» (PL) skaliraju sa tjelesnom masom (M) u skladu s teorijom geometrijske sli~nosti, i 2) da li postoje razlike
me|u spolovima u alometrijskoj povezanosti izme|u diza~kih rezultata i veli~ine tijela. U tu svrhu analizirano je deset
najboljih rezultata u WL i PL u svakoj te`inskoj kategoriji osim super-te{ke, postignutih u razdoblju 2000–2003. Podaci
su analizirani primjenom alometrijskog modela te polinomijalnog modela drugog stupnja, dok je provjera o primjerenosti primijenjenih modela provjerena detaljnom regresijskom dijagnostikom. Rezultati istra`ivanja pokazuju kako
1) `enski rezultati u WL i mu{ki rezultati u PL skaliraju s M sukladno teoriji o geometrijskoj sli~nosti, 2) postoje
zna~ajne spolne razlike u alometrijskoj povezanosti izme|u diza~kih rezultata u oba sporta i M; te su razlike vjerojatno
rezultat spolnih razlika u kompoziciji tijela, 3) rezultati u WL i PL skaliraju s M razli~ito vjerojatno zbog strukturalnih i
funkcionalnih razlika koje postoje me|u njima. Me|utim, alometrijski eksponenti dobiveni u ovom istra`ivanju ne omogu}uju definiranje indeksa rezultata u WL i PL koji su nezavisni od veli~ine tijela iz razloga {to alometrijski model
favorizira rezultate kod diza~a u srednjim te`inskim kategorijama kod ve}ine analiziranih podataka. Zbog mogu}ih
devijacija u geometrijskoj sli~nosti diza~a utega, budu}a istra`ivanja o skaliranju rezultata u WL i PL trebala bi koristiti
nemasnu masu tijela i tjelesnu visinu kao pokazatelje veli~ine tijela.
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